Well, I couldn't find him on the 1939 Register so in the end I sent for his mother's Will. Although she did not die until 1977, the Will was made in 1966, and it's clear from its contents that at that point, Claude William was still alive, as his mother left him £500 and a share of her household effects. His siblings were better provided for.
Sadly, whoever drafted the Will did not see fit to include addresses, so I still have no idea where on the planet Clause was.
I'm now trying to locate his nieces, who are named in the Will, without much success.